Third Law and Hitting Feathers

You can't hit a feather in midair with a force of 200 N because the feather is not capable of exerting a 200 N force on you. The forces "you hit feather" and "feather hits you" are a Newton's Third Law action/reaction force pair, so they must always be exactly equal in size. If an object isn't strong enough to exert a certain amount of force on you, then you can't exert that amount of force on it.​

My daughter had a slightly different version of this question in her eighth grade physics class:

Can you hit a feather in a frictionless environment with a 200N force?​

The teacher explained that "A feather could not move that fast."

I don't quite get these explanations. How would one go about calculating or determining the ability of an object to exert a particular amount of reactive force? Why can't a feather move and any speed in a "frictionless environment?"

Now just how am I going to hit this feather?
A 200N force is similar to dropping a 20kg weight on it. It'll take the feather right down to floor level and crush it.
Maybe I'll hit it with a bullet from a gun. That'll do it. Now my feather is in several pieces.
And who says a feather couldn't exert a 200N force. First I'll drop it in liquid nitrogen to make it nice and rigid then fire it from a catapult. Thud.
Or maybe wait for a tornado to come along. Those 500 mile per hour winds will turn my delicate little feather into a piece of shrapnel.
Frictionless environment? Sounds like a vacuum to me. Drop that old feather out of your space capsule at 25000 miles per hour and the next thing it ploughs into will get a hefty whack.

Thank you Carid!
If I understand you correctly: It would be difficult to impart the 200N force to the feather in a non-destructive fashion. If one were to carefully control the conditions, it would be possible to impart significant force to the feather.
The bullet case you mention is interesting. Does the fact that the feather winds up in pieces have any bearing on whether or not it can exert an opposing force? What about a larger projectile that would impact the full feather at once (e.g. a flying brick)? Would the feather not exert an opposing force on the brick? (I realize that the mass of the feather means that the effect will not be significant)

OK I don't think I was being sufficiently scientific in my reply.
Put the feather on a table. Put the 20 kilogram weight on top. This exerts a steady force of approximately 200N on the feather. The feather deforms and transmits this force to the table. The table deforms and transmits this force to the ground. The ground is deformed until it resists pushing back with a supplementary 200N force. The table transmits this to the feather, the feather to the weight. The weight stops moving down. Newton's Third Law is safe again.
Now whacking a feather floating about in the air is not the same as applying a steady force. We are supplying an impulse. Don't expect the feather to stop your cricket bat in mid-air and by supplying a similar impulse. An impulse is a force undergoing an acceleration itself.
The cricket bat moving smoothly runs into the feather. The feather being an object with a small amount of mass is accelerated, energy is imparted to it; the cricket bat being a larger object with a greater mass is slightly slowed, it has lost a tiny fraction of its initial kinetic energy. In a frictionless environment the feather should indeed bounce off the bat, but in an atmosphere like ours the enormous surface of the feather relative to its mass ensures that it loses the energy imparted to it very quickly by friction with the air.
A self-proclaimed kung-fu expert once showed me that hitting a door with a fist produced less effect in terms of movement of the door than a sustained push with one finger. He thought this remarkable. When you think about it it's not surprising at all. A small force exerted for a long time can achieve more than a stronger force exerted for a short time.

Just for clarification, in a frictionless environment why is it not possible to obtain infinite acceleration as there is no opposing forces?
I know you can't get infinite acceleration because F=ma, so infinite acceleration would give an infinite force, as well as an infinite velocity which is illogical. So what exactly is it that is stopping infinite acceleration is a frictionless environment?

What is stopping any acceleration at all? Inertia, this mysterious characteristic of mass that makes it unwilling to change its state of rest or uniform motion in a straight line. Where does inertia come from? Mach thought it a consequence of the gravitational influence of the rest of the Universe. Anyway acceleration of any mass requires energy. When the flow of energy stops so does the acceleration. There's also the little problem of relativistic mass increase as we approach speeds comparable to that of light. Photons being massless travel at light speed. Other particles have mass and can never be accelerated to light speed. The cause of this is supposed to be the Higgs field without which all particles would dash about at the speed of light and the Universe would be a VERY different place. We have yet to confirm the existence of the Higgs field. The large Hadron Collider may be able to shed light on this next year.

If I understand you correctly: In a frictionless environment if a feather would be hit with a cricket bat (never heard of one till now :) ) with a force of 200N the bat would be slowed by the feather (slightly) and the feather would be accelerated by its encounter with the bat. The speed of the feather would, I suppose be very high. Would it actually have exerted a 200N reaction force on the bat? Or does it move away from the bat before that happens (and I guess, before the bat has a "chance" to deliver a full 200N.) I am also assuming that the acceleration of the feather ceases when it bounces from the bat.

Staff: Mentor

You can't hit a feather in midair with a force of 200 N because the feather is not capable of exerting a 200 N force on you. The forces "you hit feather" and "feather hits you" are a Newton's Third Law action/reaction force pair, so they must always be exactly equal in size. If an object isn't strong enough to exert a certain amount of force on you, then you can't exert that amount of force on it.​

This is partly true and partly irrelevant. Newton's 3rd law is certainly true. If something exerts a 200 N force on the feather, then the feather exerts a 200 N force on that something.

My daughter had a slightly different version of this question in her eighth grade physics class:

Can you hit a feather in a frictionless environment with a 200N force?​

The teacher explained that "A feather could not move that fast."

I'd say just the opposite. One reason why it's very difficult to swat a feather hard (with your fist, say) is that the feather accelerates all too easily. You just can't move your hand fast enough to maintain solid contact. (It's easy to exert a 200 N force against a wall, since it's not going anywhere.)

The problem here lies with your everyday experience with feathers. When you 'hit' a feather, it gently floats around as if you hardly exerted any force on it at all, probably due to the reason Doc Al mentioned.
However, this is due to the feather being surround by air, and the feather having very low density and relatively big frontal area, it loses it's momentum rather fast to the surrounding air due to friction. Look up Stokes' law to gain some more understanding in (idealised) moving particle with friction situations if you'd like.
However, if you'd hit a feather in a frictionless (usually vacuum) environment, you'd transfer momentum from your hand/bat/bullet to the feather and it would gain a pretty high velocity. If you managed to push it untill you exerted 200 N it would go pretty fast as well, but this is more difficult because the feather has low inertia (low mass) so it's more than happy to accelerate when you exert force on it, so it will pretty soon be moving too fast for you to keep up with it and exert more force on it (as Doc Al said earler).